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"" 1 "" {XPPMATH 20 "6'%/in~the~time~t=G\"#O%2month~I~will~haveG$\"+P+
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20 "6'%/in~the~time~t=G\"#P%2month~I~will~haveG$\"+ODp%)R!\"'%>$~,~it~
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me~t=G\"#Q%2month~I~will~haveG$\"+lm#45%!\"'%>$~,~it~is~not~bad,~is~no
t~it?G" }}{PARA 11 "" 1 "" {XPPMATH 20 "6'%/in~the~time~t=G\"#R%2month
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11 "" 1 "" {XPPMATH 20 "6'%/in~the~time~t=G\"#S%2month~I~will~haveG$\"
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{XPPMATH 20 "6'%/in~the~time~t=G\"#T%2month~I~will~haveG$\"+!4yCX%!\"'
%>$~,~it~is~not~bad,~is~not~it?G" }}{PARA 11 "" 1 "" {XPPMATH 20 "6'%/
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ad,~is~not~it?G" }}{PARA 11 "" 1 "" {XPPMATH 20 "6'%/in~the~time~t=G\"
#V%2month~I~will~haveG$\"+(HR#*o%!\"'%>$~,~it~is~not~bad,~is~not~it?G
" }}{PARA 11 "" 1 "" {XPPMATH 20 "6'%/in~the~time~t=G\"#W%2month~I~wil
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"" {XPPMATH 20 "6'%/in~the~time~t=G\"#X%2month~I~will~haveG$\"+AO$z#\\
!\"'%>$~,~it~is~not~bad,~is~not~it?G" }}{PARA 11 "" 1 "" {XPPMATH 20 "
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1 "" {XPPMATH 20 "6'%/in~the~time~t=G\"#\\%2month~I~will~haveG$\"+!*[=
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20 "6'%/in~the~time~t=G\"#]%2month~I~will~haveG$\"+D2BLb!\"'%>$~,~it~i
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11 "" 1 "" {XPPMATH 20 "6'%/in~the~time~t=G\"#`%2month~I~will~haveG$\"
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{XPPMATH 20 "6'%/in~the~time~t=G\"#a%2month~I~will~haveG$\"+gmSEg!\"'%
>$~,~it~is~not~bad,~is~not~it?G" }}{PARA 11 "" 1 "" {XPPMATH 20 "6'%/i
n~the~time~t=G\"#b%2month~I~will~haveG$\"+&)*e4:'!\"'%>$~,~it~is~not~b
ad,~is~not~it?G" }}{PARA 11 "" 1 "" {XPPMATH 20 "6'%/in~the~time~t=G\"
#c%2month~I~will~haveG$\"+](=gF'!\"'%>$~,~it~is~not~bad,~is~not~it?G" 
}}{PARA 11 "" 1 "" {XPPMATH 20 "6'%/in~the~time~t=G\"#d%2month~I~will~
haveG$\"+D!)e,k!\"'%>$~,~it~is~not~bad,~is~not~it?G" }}{PARA 11 "" 1 "
" {XPPMATH 20 "6'%/in~the~time~t=G\"#e%2month~I~will~haveG$\"+&))ow_'!
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'%/in~the~time~t=G\"#f%2month~I~will~haveG$\"+:MEam!\"'%>$~,~it~is~not
~bad,~is~not~it?G" }}{PARA 11 "" 1 "" {XPPMATH 20 "6'%/in~the~time~t=G
\"#g%2month~I~will~haveG$\"+0PP\"y'!\"'%>$~,~it~is~not~bad,~is~not~it?
G" }}{PARA 11 "" 1 "" {XPPMATH 20 "6'%/in~the~time~t=G\"#h%2month~I~wi
ll~haveG$\"+g=+4p!\"'%>$~,~it~is~not~bad,~is~not~it?G" }}{PARA 11 "" 
1 "" {XPPMATH 20 "6'%/in~the~time~t=G\"#i%2month~I~will~haveG$\"+&)*\\
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20 "6'%/in~the~time~t=G\"#j%2month~I~will~haveG$\"++-#e;(!\"'%>$~,~it~
is~not~bad,~is~not~it?G" }}{PARA 11 "" 1 "" {XPPMATH 20 "6'%/in~the~ti
me~t=G\"#k%2month~I~will~haveG$\"+NY,&H(!\"'%>$~,~it~is~not~bad,~is~no
t~it?G" }}{PARA 11 "" 1 "" {XPPMATH 20 "6'%/in~the~time~t=G\"#l%2month
~I~will~haveG$\"+DatCu!\"'%>$~,~it~is~not~bad,~is~not~it?G" }}{PARA 
11 "" 1 "" {XPPMATH 20 "6'%/in~the~time~t=G\"#m%2month~I~will~haveG$\"
+:Z)\\b(!\"'%>$~,~it~is~not~bad,~is~not~it?G" }}{PARA 11 "" 1 "" 
{XPPMATH 20 "6'%/in~the~time~t=G\"#n%2month~I~will~haveG$\"+bYw&o(!\"'
%>$~,~it~is~not~bad,~is~not~it?G" }}{PARA 11 "" 1 "" {XPPMATH 20 "6'%/
in~the~time~t=G\"#o%2month~I~will~haveG$\"+5u2<y!\"'%>$~,~it~is~not~ba
d,~is~not~it?G" }}{PARA 11 "" 1 "" {XPPMATH 20 "6'%/in~the~time~t=G\"#
p%2month~I~will~haveG$\"+X^#*[z!\"'%>$~,~it~is~not~bad,~is~not~it?G" }
}{PARA 11 "" 1 "" {XPPMATH 20 "6'%/in~the~time~t=G\"#q%2month~I~will~h
aveG$\"+]+J\"3)!\"'%>$~,~it~is~not~bad,~is~not~it?G" }}{PARA 11 "" 1 "
" {XPPMATH 20 "6'%/in~the~time~t=G\"#r%2month~I~will~haveG$\"+0VB9#)!
\"'%>$~,~it~is~not~bad,~is~not~it?G" }}{PARA 11 "" 1 "" {XPPMATH 20 "6
'%/in~the~time~t=G\"#s%2month~I~will~haveG$\"+5,qZ$)!\"'%>$~,~it~is~no
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G" }}{PARA 11 "" 1 "" {XPPMATH 20 "6'%/in~the~time~t=G\"#u%2month~I~wi
ll~haveG$\"++_E;')!\"'%>$~,~it~is~not~bad,~is~not~it?G" }}{PARA 11 "" 
1 "" {XPPMATH 20 "6'%/in~the~time~t=G\"#v%2month~I~will~haveG$\"+I*o8v
)!\"'%>$~,~it~is~not~bad,~is~not~it?G" }}{PARA 11 "" 1 "" {XPPMATH 20 
"6'%/in~the~time~t=G\"#w%2month~I~will~haveG$\"+&3Bq)))!\"'%>$~,~it~is
~not~bad,~is~not~it?G" }}{PARA 11 "" 1 "" {XPPMATH 20 "6'%/in~the~time
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it?G" }}{PARA 11 "" 1 "" {XPPMATH 20 "6'%/in~the~time~t=G\"#y%2month~I
~will~haveG$\"+l;**f\"*!\"'%>$~,~it~is~not~bad,~is~not~it?G" }}{PARA 
11 "" 1 "" {XPPMATH 20 "6'%/in~the~time~t=G\"#z%2month~I~will~haveG$\"
++1J(H*!\"'%>$~,~it~is~not~bad,~is~not~it?G" }}{PARA 11 "" 1 "" 
{XPPMATH 20 "6'%/in~the~time~t=G\"#!)%2month~I~will~haveG$\"+&)*)=N%*!
\"'%>$~,~it~is~not~bad,~is~not~it?G" }}{PARA 11 "" 1 "" {XPPMATH 20 "6
'%/in~the~time~t=G\"#\")%2month~I~will~haveG$\"+5\"HOd*!\"'%>$~,~it~is
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11 "" 1 "" {XPPMATH 20 "6'%/in~the~time~t=G\"#%)%2month~I~will~haveG$
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{XPPMATH 20 "6'%/in~the~time~t=G\"#&)%2month~I~will~haveG$\"+&G0L,\"!
\"&%>$~,~it~is~not~bad,~is~not~it?G" }}{PARA 11 "" 1 "" {XPPMATH 20 "6
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G\"#()%2month~I~will~haveG$\"+3&>;/\"!\"&%>$~,~it~is~not~bad,~is~not~i
t?G" }}{PARA 11 "" 1 "" {XPPMATH 20 "6'%/in~the~time~t=G\"#))%2month~I
~will~haveG$\"+%>je0\"!\"&%>$~,~it~is~not~bad,~is~not~it?G" }}{PARA 
11 "" 1 "" {XPPMATH 20 "6'%/in~the~time~t=G\"#*)%2month~I~will~haveG$
\"+5\\;q5!\"&%>$~,~it~is~not~bad,~is~not~it?G" }}{PARA 11 "" 1 "" 
{XPPMATH 20 "6'%/in~the~time~t=G\"#!*%2month~I~will~haveG$\"+%*[_%3\"!
\"&%>$~,~it~is~not~bad,~is~not~it?G" }}{PARA 11 "" 1 "" {XPPMATH 20 "6
'%/in~the~time~t=G\"#\"*%2month~I~will~haveG$\"+#QV*)4\"!\"&%>$~,~it~i
s~not~bad,~is~not~it?G" }}{PARA 11 "" 1 "" {XPPMATH 20 "6'%/in~the~tim
e~t=G\"##*%2month~I~will~haveG$\"+81U86!\"&%>$~,~it~is~not~bad,~is~not
~it?G" }}{PARA 11 "" 1 "" {XPPMATH 20 "6'%/in~the~time~t=G\"#$*%2month
~I~will~haveG$\"+Eo&z7\"!\"&%>$~,~it~is~not~bad,~is~not~it?G" }}{PARA 
11 "" 1 "" {XPPMATH 20 "6'%/in~the~time~t=G\"#%*%2month~I~will~haveG$
\"+iAbU6!\"&%>$~,~it~is~not~bad,~is~not~it?G" }}{PARA 11 "" 1 "" 
{XPPMATH 20 "6'%/in~the~time~t=G\"#&*%2month~I~will~haveG$\"+gr?d6!\"&
%>$~,~it~is~not~bad,~is~not~it?G" }}{PARA 11 "" 1 "" {XPPMATH 20 "6'%/
in~the~time~t=G\"#'*%2month~I~will~haveG$\"+k<#><\"!\"&%>$~,~it~is~not
~bad,~is~not~it?G" }}{PARA 11 "" 1 "" {XPPMATH 20 "6'%/in~the~time~t=G
\"#(*%2month~I~will~haveG$\"+=jp'=\"!\"&%>$~,~it~is~not~bad,~is~not~it
?G" }}{PARA 11 "" 1 "" {XPPMATH 20 "6'%/in~the~time~t=G\"#)*%2month~I~
will~haveG$\"+m5`,7!\"&%>$~,~it~is~not~bad,~is~not~it?G" }}{PARA 11 "
" 1 "" {XPPMATH 20 "6'%/in~the~time~t=G\"#**%2month~I~will~haveG$\"+_i
U;7!\"&%>$~,~it~is~not~bad,~is~not~it?G" }}{PARA 11 "" 1 "" {XPPMATH 
20 "6'%/in~the~time~t=G\"$+\"%2month~I~will~haveG$\"+A@QJ7!\"&%>$~,~it
~is~not~bad,~is~not~it?G" }}{PARA 11 "" 1 "" {XPPMATH 20 "6'%/in~the~t
ime~t=G\"$,\"%2month~I~will~haveG$\"+C*)RY7!\"&%>$~,~it~is~not~bad,~is
~not~it?G" }}{PARA 11 "" 1 "" {XPPMATH 20 "6'%/in~the~time~t=G\"$-\"%2
month~I~will~haveG$\"+3pZh7!\"&%>$~,~it~is~not~bad,~is~not~it?G" }}
{PARA 11 "" 1 "" {XPPMATH 20 "6'%/in~the~time~t=G\"$.\"%2month~I~will~
haveG$\"+?jhw7!\"&%>$~,~it~is~not~bad,~is~not~it?G" }}{PARA 11 "" 1 "
" {XPPMATH 20 "6'%/in~the~time~t=G\"$/\"%2month~I~will~haveG$\"+7u\"=H
\"!\"&%>$~,~it~is~not~bad,~is~not~it?G" }}{PARA 11 "" 1 "" {XPPMATH 
20 "6'%/in~the~time~t=G\"$0\"%2month~I~will~haveG$\"+O/328!\"&%>$~,~it
~is~not~bad,~is~not~it?G" }}{PARA 11 "" 1 "" {XPPMATH 20 "6'%/in~the~t
ime~t=G\"$1\"%2month~I~will~haveG$\"+VcSA8!\"&%>$~,~it~is~not~bad,~is~
not~it?G" }}{PARA 11 "" 1 "" {XPPMATH 20 "6'%/in~the~time~t=G\"$2\"%2m
onth~I~will~haveG$\"+(G$zP8!\"&%>$~,~it~is~not~bad,~is~not~it?G" }}
{PARA 11 "" 1 "" {XPPMATH 20 "6'%/in~the~time~t=G\"$3\"%2month~I~will~
haveG$\"+AOC`8!\"&%>$~,~it~is~not~bad,~is~not~it?G" }}}{EXCHG {PARA 0 
"" 0 "" {TEXT -1 110 "We have recursive equation, which can be solved \+
(it means we can find the explicite rule) using comand rsolve:" }}}
{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 62 "Z:='Z';t:='t';zeta:='zeta';
\neq:=Z(0)=0,Z(t)=Z(t-1)*(1+zeta)+x;" }}{PARA 11 "" 1 "" {XPPMATH 20 "
6#>%\"ZGF$" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%\"tGF$" }}{PARA 11 "" 
1 "" {XPPMATH 20 "6#>%%zetaGF$" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%#e
qG6$/-%\"ZG6#\"\"!F*/-F(6#%\"tG,&*&-F(6#,&F.\"\"\"F4!\"\"F4,&F4F4%%zet
aGF4F4F4\"$+\"F4" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 28 "xxx:=Z(
t)=rsolve(\{eq\},Z(t));" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%$xxxG/-%
\"ZG6#%\"tG,&*(\"$+\"\"\"\"%%zetaG!\"\"),&F-F-F.F-F)F-F-*&F,F-F.F/F/" 
}}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 41 "evalf(subs(t=108,zeta = .
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+sOC`8!\"&" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 51 "Summing of the futu
re value of all of the payments:" }}}{EXCHG {PARA 0 "> " 0 "" 
{MPLTEXT 1 0 34 "f:=sum(x*(1+zeta)^tau,tau=0..t-1);" }}{PARA 11 "" 1 "
" {XPPMATH 20 "6#>%\"fG,&*(\"$+\"\"\"\"%%zetaG!\"\"),&F(F(F)F(%\"tGF(F
(*&F'F(F)F*F*" }}}{EXCHG }{EXCHG }{EXCHG {PARA 0 "" 0 "" {TEXT -1 49 "
The results is (as we hope and suppose) the same." }}}{EXCHG {PARA 0 "
> " 0 "" {MPLTEXT 1 0 40 "plot(subs(zeta=.004074124,f),t=1..12*9);" }}
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Fhq$\"3$>JDDv%HTfFh^l7$F[r$\"3*y%QLTJ7DmFh^l7$F^r$\"3@.6x^T^RuFh^l7$Fa
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Fjr$\"3_%3,Zf))G:\"F^`u7$F]s$\"37ZO2C_%eG\"F^`u7$F`s$\"3Z(=oH::7W\"F^`
u7$Fcs$\"3_.X0<fI3;F^`u7$Ffs$\"3%4ov`xd*)z\"F^`u7$Fis$\"3T#>KU=q+,#F^`
u7$F\\t$\"3&z#>7anfDAF^`u7$F_t$\"3b)\\!GFz*3]#F^`u7$Fbt$\"3%=qN\\h/cx#
F^`u7$Fft$\"3q@=&\\W]:5$F^`u7$Fcix$\"3[MQ`+/sqKF^`u7$Fit$\"3QJl&zQe!\\
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{XPPMATH 20 "6#>%\"xGF$" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%\"fG/%\"Z
G*(%\"xG\"\"\",&),&F)F)%%zetaGF)%\"tGF)F)!\"\"F)F-F/" }}}{EXCHG {PARA 
0 "> " 0 "" {MPLTEXT 1 0 27 "x=solve(f,x);\nt=solve(f,t);" }}{PARA 11 
"" 1 "" {XPPMATH 20 "6#/%\"xG*(%\"ZG\"\"\"%%zetaGF',&),&F'F'F(F'%\"tGF
'F'!\"\"F-" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#/%\"tG*&-%#lnG6#*&,&*&%
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{PARA 0 "> " 0 "" {MPLTEXT 1 0 19 "zeta=solve(f,zeta);" }}{PARA 11 "" 
1 "" {XPPMATH 20 "6#/%%zetaG-%'RootOfG6#,(*&%\"ZG\"\"\"%#_ZGF+F+*&%\"x
GF+),&F+F+F,F+%\"tGF+!\"\"F.F+" }}}{EXCHG {PARA 15 "" 0 "" {TEXT -1 
31 "t... time of saving (in months)" }}{PARA 15 "" 0 "" {TEXT -1 35 "x
 ... money I will sawe every month" }}{PARA 15 "" 0 "" {TEXT -1 44 "Z \+
... money I vill have on the end of saving" }}{PARA 15 "" 0 "" 
{XPPEDIT 18 0 "epsilon;" "6#%(epsilonG" }{TEXT -1 45 " ... interest ra
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0 79 "xxx:=subs(t=15*12,x=1000,Z=1290000,f );\nepsilon:=fsolve(xxx);\n
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{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 61 "t:='t';\nF:=unapply(subs(t=9
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#>%\"tGF$" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%\"FGj+6#%%zetaG6\"6$%)o
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